The IBC, for example, has a time limitation for building permits, after which time the permits expire. Any work after the permit expires would be considered work without a permit and any locally adopted fee/penalty for work without a permit would apply.

If the structure was not completed (for whatever reasons) and the permit expired, all new work would be required to meet the code at the time a permit for the new work was applied for, and if the work to finish the structure exceeded 50% of the value of the structure prior to finishing it, i.e., its value as an abandoned structure for whatever work had been done and was such that the work would be allowed to remain, then the work would be considered a substantial improvement, which would require that the entire structure (including the previously constructed abandoned parts) would need to meet current code, and would thus require all the associated fees with those permits.

The codes do not address fees as to dollar amount and for what, only that the local AHJ applies the locally adopted fee schedule to the permitting costs.

Basically, it depends on what your AHJ has adopted for fees to address the above issues.